A factory has been using three different machines to produce ball bearings. The

Question

A factory has been using three different machines to produce ball bearings. The ball bearings can be used if they
have a diameter between 9-11mm. The specs of the 3 machines are:
• New machine: = 10mm, = 0.5mm
• Old machine: = 10mm, = 1mm
• Borrowed machine: =9, = 0.3mm

a) For each machine compute the probability of producing a useful ball bearing
(6 marks)

c) Given the fact that a randomly selected ball bearing turns out to be usable, what is the probability that it was

made on the new machine?

Useable (U Non Useable New machine (N) Old machine (O) Borrowed machine (B)

Explanation / Answer

Ans:

a)

b)From the above table we know that :

P(usable/new)=0.9545

P(usable and new)/P(new)=0.9545

P(usable and new)=0.9545*0.7=0.66815

P(Non usable and new)=0.7-0.66815=0.03185

Similarly calculate other entries as below:

c)P(new machine/usable)=P(usable and new)/P(usable)=0.66815/0.85469=0.7817

mean std dev z(9) z(11) P(11)-P(9) New 10 0.5 -2 2.0000 0.9545 Old 10 1 -1 1.0000 0.6827 Borrowed 9 0.3 0 6.6667 0.5000

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.